Unital Dilations of Completely Positive Semigroups: From Combinatorics to Continuity

Abstract

Using ideas due to Jean-Luc Sauvageot, we prove the existence of a continuous unital dilation of a CP$_0$-semigroup on a separable W$^*$-algebra. This paper presents the material in the author's Ph. D. thesis (arXiv.org:1304.0134.pdf) with some generalizations and an improved exposition.Comment: 69 pages. Submitted to Memoirs of the AM